- The average is 10 people per month, which is within acceptable limits. (OK to use)
- The average of 10 people per month is within acceptable limits. (OK to use)
- The average is of 10 people per month, which is within acceptable limits. (Not OK to use)
The first sentence tells me the result of calculating the average. It was 10 people per month.
The second sentence tells me that the average, which happens to be 10 people per month, is OK. I could also say "The average is OK."
The third sentence isn't something I would recommend using. It's not obviously ungrammatical, but it isn't meaningful in AmE. I have seen some results in apparently well-written documents, but the usage seems almost exclusive to Indian English, like this book.
The third sentence could mean the average is calculated from some sample of 10 people per month, but it's really confusing how you would average people together. You have to calculate the average test score, or the average weight, or some other measurable characteristic of a person.
The only way I can think of to use "The average is of" in a meaningful sentence is like this:
I calculated some statistics for my paper. One average is of the length of the sentences where the word 'however' is used. That average is much higher than the average length of the sentences without the word 'however'.
A more common way of writing it would be:
I calculated some statistics for my paper. I averaged the length of the sentences where the word 'however' is used. That average is much higher than the average length of the sentences without the word 'however'.
The only way I can think of to interpret "the average is of" is that it is explaining what group of things the average was calculated using. I compare it to "The photo is of my family." which means the picture is a representation of my family and it isn't equivalent to my family. An average that "is of something" is a representation of that something but the average doesn't equal that something.
Some other ways that this could show up in a search, but not have the same sense as sentence #3:
The average is, of course, 50% of the total. (Many people are allergic to commas and so you might see this without punctuation)
The average is of interest because it is a good estimate of what we might expect in most circumstances.
Now the average is of around 210 pieces, but there are already companies above the 225 mark.Source (I think I would prefer "The average is around/about/approximately 210 pieces")